Combine 1/2 cup of the blackberries, the shallots, garlic, honey, mustard, and vinegars in a blender and process on high for 10 seconds. Stop and scrape down the sides before continuing. With the machine running, slowly drizzle the oil into the blender until the mixture is slightly thickened and smooth. Adjust the seasonings with salt and freshly ground black pepper, to taste. Strain the dressing through a fine-meshed sieve into a clean container. Set aside until ready to serve, or store in the refrigerator for up to 1 week. Makes about 1 cup. Serve over mixed greens with toasted walnuts.